The paired data below consists
The paired data below consists of heights and weights of 6randomly selected adults. The equation of the regression line isy-hat = -181.342 + 144.46x and the standard error of estimate isse=5.0015. Find the 95% prediction interval for the weight of aperson whose height is 1.75 m.
x height (meters) y weight (kg)
1.61 54
1.72 62
1.78 70
1.80 84
1.67 61
1.88 92
Answer:
= (1.61 +1.72 + 1.78 + 1.80 + 1.67 + 1.88) / 6 = 1.743333
= (1.61 – 1.743333)2 + (1.72 -1.743333)2 + (1.78- 1.743333)2+ (1.80- 1.743333)2 + (1.67-1.743333)2 + (1.88- 1.743333)2
= 0.04693333
yp = -181.342 + 144.46 * 1.75 = 71.463
Degree of freedom , df = n-2 = 6 – 2 = 4
t value of 95% prediction interval and df = 4 is 2.78
95% prediction interval for the weight of a person whose heightis 1.75 is
yp 
t * se * 
= 71.463 2.78 * 5.0015 *
= 71.463 2.78 * 5.0015 *1.080562
= 71.463 15.02432
= (71.463 – 15.02432, 71.463 + 15.02432)
= (56.43868, 86.48732)
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